Wednesday, June 18, 2014

Poker: An Overview

Hand Ranges

I was doing some house keeping the other day and decided to re-look at my hand ranges to open and raise in a 9 handed game:
  • UTG (7% for 2 opponents) 77+, ATs/AQo+, KQs
  • UTG+1 (10% for 2 opponents) 77+, A9s/AJo+,  KTs+/KQo, QJs
  • UTG+2 (14% for 2 opponents) 66+, A7s/ATo+, K9s/KJo+, QTs+, JTs
  • MP1 lowjack (20% for 2 opponents) 55+, A3s/A8o+, K7s/KTo+, Q9s+/QJo, JTs
  • MP2 highjack (25% for 1 opponent) 44+, Axs/A7o+/A5o, K6s/K9o+, Q9s/QTo+, JTs
  • cutoff (35% for 1 opponent) 33+, Ax, K3s/K7o+, Q6s/9o+, J8s+/JTo, T9s
  • dealer (50% for 1 opponent) 22+, Ax, Kx, Qxs/Q5o+, J5s/J8o+, T7s+/T9o, 98s
  • SB (50)
We can see this gives an attempt to steal of ~40-45% over the cutoff/dealer/SB positions. This sounds slightly high but still reasonable in online poker. Notice that our range is also skewed to play less OOP and more IP, because I just find it to be easier that way. This is in comparison to a "typical" opening range for UTG to SB: 12/14/16/19/24/31/45/60. ie. open UTG with 12% and hands, open UTG+1 with 14% of hands etc.

Using our opponent's "typical" opening range, we can calculate how frequently we will open: (7% + 0.88*10% + 0.88*0.86*14% + 0.88*0.86*0.84*20% + 0.88*0.86*0.84*0.81*25% + 0.88*0.86*0.84*0.81*0.76*35% + 0.88*0.86*0.84*0.81*0.76*0.69*50% + 0.88*0.86*0.84*0.81*0.76*0.69*0.55*50%) / 9 = (7% + 0.88*10% + 0.7568*14% + 0.6357*20% + 0.5149*25% + 0.3913*35% + 0.2700*50% + 0.1485*50%) / 9 = 8.8%

Now also consider the number of times that we 3bet. Roughly, we should 3bet if we are in the top half of the range of the raiser. Instead, let us approximate by saying we are going to 3bet/call raises with the top half of our own open raise range for that position (UTG+1 to dealer). From SB and BB, let's say we will play top 5% of range. Let us approximate our 3bet/call frequency as follows:
(0.12*5% + 0.25*7% + 0.36*10% + 0.49*14% + 0.6*20% + 0.73*25% + 0.85*5% + 0.95*5%) / 9 = 6%

This means we have a VP$IP of very roughly 14%-15%. Tracking my own statistics, I see that I have a VP$IP between 12%-20% each session, and PFR 10%-16%. This sounds roughly inline with what we looked at above (a bit looser) and points to a roughly 50/50 split between 3betting (3%) vs calling (3%) when facing a raise. Whereas previously, most of the calling came from set mining OOP because I was getting say 1:3 odds, I am working on reducing that and instead changing some IP 3bets into flat calling to limit pot sizing, especially against calling stations.

Bet Sizing

Preflop Bet Sizing
Whereas previously I have employed a 3bb bet sizing for late position steals, recently I am testing out a smaller size so the pot doesn't get too bloated. I've frequently had hands before where SPR gets so low that I am committed with mediocre hands.
  • 2bb for UTG, UTG+1, UTG+2
  • 2.5bb MP and LP
  • 3.5bb in SB
For 3bets, I tend to do a bit over half pot if IP and close to full pot if OOP.

Flop Cbet Sizing
Previously, I always ran into trouble betting 1x pot OOP because I would lose pots like overpairs/two pairs against sets or better. That itself is not an issue, but I would be way too committed to fold by the time the opponent showed enough strength/their hand range had clarified to the pt where I am behind/have < 50% equity. Hopefully, the smaller preflop bet sizing should help with the "Bayesian updating" before the pot gets too big. In a 3betted/4betted pot though, I might have to check-call more often on the flop/turn/river, or use 1/2x pot bet sizes.
  • OOP- usually 1x pot
  • IP- usually 1/2x pot
  • adjust size up by 1.5x-2x of normal bet if flop is super wet
  • adjust down to 2/3-1/2x if the flop is super dry
However, I have not thought very deeply on how to incorporate probe bets into flop betting yet. Also, what % of flops should you cbet, and what % should you check raise/call/fold? Should your hand range or bet sizes change as the effective stack size changes? I hope to think about these points in another article.